We use a football because it is the kind of ball easily kicked with the foot. Since the game involved feet and balls (and referees to point out the balls you score points with) "football" seemed a natural name.

I can sympathise (or even sympathize) with holdy-runny-oblong-unless-the-coach-says-different-in-your-in-ear-monitor-hut-hut-hut for needing a different name, but that one was already taken.